Nematic order experimental determination

A prerequisite for experimental determination of the anisotropic electrooptic properties (Ae, An) is the occurrence of a nematic phase with a defined order parameter S [4]. As single substances, many commercially used liquid crystalline materials have either no mesophase or a smectic phase only. As components of nematic basic mixtures on the other hand, they behave like typical liquid crystals. 

The order parameter can be directly related to certain experimentally determinable quantities - say, for example, the diamagnetic anisotropy of the liquid crystal.Let us choose a space-fixed cartesian coordinate system xyz with z parallel to n. If and are the principal diamagnetic susceptibilities of the molecule referred to its own principal axes, the average z component of the susceptibility per unit volume in the nematic phase is evidently... 

By making use of the form of the Landau energy proposed by de Gennes [17], all coefficients in this expression have been evaluated from experimental data [4]. Using these data to calculate U, one obtains a value that is considerably smaller than the one determined from the linearized analysis outlined above. As has been noted, however, a consistent analysis should not only include terms quadratic in the strains and bilinear coupling terms of the order parameter and the strain, but rather also nonlinear effects as well as nonlinear coupling terms between strain and the nematic order parameter [4]. 

Due to a pronounced optical anisotropy of ordered liquid crystals, reflection elhpsometry is a powerful experimental tool for the study of surface-modified liquid crystalline order. The sensitivity of the technique enables quantitative measurements of the nematic order parameter profile at the interfaces. Prom observation of the nematic wetting of the solid-liquid crystal interface, we have determined the values of the coupling energies between the surface and the nematic order. Even the pretransitional effects at solid-smectic liquid crystals can be studied with elhpsometry due to the strong coupling between the nematic and the smectic order. The time evolution of the complex structure of the liquid crystal adsorbate on a solid substi ate has also been successfully monitored using BAE. 

To extract concrete predictions for experimental parameters from our calculations is a non-trivial task, because neither the energetic constant B nor the rotational viscosity yi are used for the hydrodynamic description of the smectic A phase (but play an important role in our model). Therefore, we rely here on measurements in the vicinity of the nematic-smectic A phase transition. Measurements on LMW liquid crystals made by Litster [33] in the vicinity of the nematic-smectic A transition indicate that B is approximately one order of magnitude less than Bo. As for j we could not find any measurements which would allow an estimate of its value in the smectic A phase. In the nematic phase y increases drastically towards the nematic-smectic A transition (see, e.g., [51]). Numerical simulations on a molecular scale are also a promising approach to determine these constants [52],... 

In this Chapter we introduce some of the theoretical approaches for studying thin nematic liqnid crystalline systems, both on the microscopic and macroscopic level. In the former, one models the microscopic interactions between the constituing molecules, leaves the system to evolve, and then determines its macroscopic properties. If the obtained macroscopic behaviour is in agreement with the experimental evidence the modeled interaction is considered appropriate. On the other hand, the macroscopic description takes into account the universal properties of systems in the vicinity of phase and structural transitions. This means that they are based on the fact that in the vicinity of phase changes the macroscopic properties of the system do not depend on the details of the microscopic interactions but on the symmetry properties and dimensionality of the system in question. Most of our attention is focused on the effects of confinement on to liquid crystalline order. Finally, we will be interested in the resulting disjoining pressure. The evidences in experiments will be briefly mentioned. 

The order parameter is a theoretical tool that can be measured experimentally. It is possible to determine the anisotropy of a particular property for a nematic relative to the anisotropy of a perfectly aligned material. Consider a molecule lying at an angle u to as indicated below ... 

Recently, phase behaviour of mixtures consisting of a polydisperse polymer (polystyrene) and nematic liquid crystals (p-ethoxy-benzylidene-p-n-butylani-line) was calculated and determined experimentally. The former used a semi-empirical model based on the extended Flory-Huggins model in the framework of continuous thermodynamics and predicted the nematic-isotropic transition. The model was improved with a modified double-lattice model including Maier-Saupe theory for anisotropic ordering and able to describe isotropic mixing. ... 

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